
This state can be prepared by a Euclidean path integral over an interval of length \(\beta /2\)  in Euclidean time. In a holographic system, an uncharged black hole provides a bulk saddle-point for these Euclidean boundary conditions; in situations where this is the dominant saddle-point, on continuation to the Lorentzian picture the eternal maximally extended black hole then provides the dual description of the state (). This connection is a key motivating example for the idea that entanglement is related to connection of the bulk geometry [1]}. There are two-point functions involving operators in the two copies of the system \(\langle \mathcal {O}_L \mathcal {O}_R \rangle \)  which have non-zero values in this state; in the connected bulk geometry, influences can propagate from one boundary to the other, while in the boundary quantum theory, the two-point functions can be non-vanishing in the absence of any interaction due to the entanglement of the state [2]}.
